For increasing the cooling performance within the system with one circular hot wall, combinations of nanotechnology and Kelvin force have been utilized. Iron oxide with fraction of 0.04 has been added to water and properties were estimated according to homogenous model. Appearance of wire near the middle of circular wall generates space-dependent Kelvin force which acts like gravity force and boosts the migration of ferrofluid. To gain the solution, CVFEM was applied to measure the values of scalars. Before employment of numerical approach, the equations become simplified with defining the vorticity formulation. Utilizing FHD makes the fluid move faster inside the domain and more effective collision with walls happens. Nu elevates about 108.05% by applying FHD when [Formula: see text]. When [Formula: see text] and 4e3, imposing greater buoyancy forces offers augmentation of Nu about 11.54% and 0.01%. Utilizing ferrofluid instead of H2O makes Nu to rise around 14.15%.